Major fixes and new features

venv/lib/python3.12/site-packages/mypy/graph_utils.py

@@ -0,0 +1,112 @@
+"""Helpers for manipulations with graphs."""
+
+from __future__ import annotations
+
+from typing import AbstractSet, Iterable, Iterator, TypeVar
+
+T = TypeVar("T")
+
+
+def strongly_connected_components(
+    vertices: AbstractSet[T], edges: dict[T, list[T]]
+) -> Iterator[set[T]]:
+    """Compute Strongly Connected Components of a directed graph.
+
+    Args:
+      vertices: the labels for the vertices
+      edges: for each vertex, gives the target vertices of its outgoing edges
+
+    Returns:
+      An iterator yielding strongly connected components, each
+      represented as a set of vertices.  Each input vertex will occur
+      exactly once; vertices not part of a SCC are returned as
+      singleton sets.
+
+    From https://code.activestate.com/recipes/578507/.
+    """
+    identified: set[T] = set()
+    stack: list[T] = []
+    index: dict[T, int] = {}
+    boundaries: list[int] = []
+
+    def dfs(v: T) -> Iterator[set[T]]:
+        index[v] = len(stack)
+        stack.append(v)
+        boundaries.append(index[v])
+
+        for w in edges[v]:
+            if w not in index:
+                yield from dfs(w)
+            elif w not in identified:
+                while index[w] < boundaries[-1]:
+                    boundaries.pop()
+
+        if boundaries[-1] == index[v]:
+            boundaries.pop()
+            scc = set(stack[index[v] :])
+            del stack[index[v] :]
+            identified.update(scc)
+            yield scc
+
+    for v in vertices:
+        if v not in index:
+            yield from dfs(v)
+
+
+def prepare_sccs(
+    sccs: list[set[T]], edges: dict[T, list[T]]
+) -> dict[AbstractSet[T], set[AbstractSet[T]]]:
+    """Use original edges to organize SCCs in a graph by dependencies between them."""
+    sccsmap = {v: frozenset(scc) for scc in sccs for v in scc}
+    data: dict[AbstractSet[T], set[AbstractSet[T]]] = {}
+    for scc in sccs:
+        deps: set[AbstractSet[T]] = set()
+        for v in scc:
+            deps.update(sccsmap[x] for x in edges[v])
+        data[frozenset(scc)] = deps
+    return data
+
+
+def topsort(data: dict[T, set[T]]) -> Iterable[set[T]]:
+    """Topological sort.
+
+    Args:
+      data: A map from vertices to all vertices that it has an edge
+            connecting it to.  NOTE: This data structure
+            is modified in place -- for normalization purposes,
+            self-dependencies are removed and entries representing
+            orphans are added.
+
+    Returns:
+      An iterator yielding sets of vertices that have an equivalent
+      ordering.
+
+    Example:
+      Suppose the input has the following structure:
+
+        {A: {B, C}, B: {D}, C: {D}}
+
+      This is normalized to:
+
+        {A: {B, C}, B: {D}, C: {D}, D: {}}
+
+      The algorithm will yield the following values:
+
+        {D}
+        {B, C}
+        {A}
+
+    From https://code.activestate.com/recipes/577413/.
+    """
+    # TODO: Use a faster algorithm?
+    for k, v in data.items():
+        v.discard(k)  # Ignore self dependencies.
+    for item in set.union(*data.values()) - set(data.keys()):
+        data[item] = set()
+    while True:
+        ready = {item for item, dep in data.items() if not dep}
+        if not ready:
+            break
+        yield ready
+        data = {item: (dep - ready) for item, dep in data.items() if item not in ready}
+    assert not data, f"A cyclic dependency exists amongst {data!r}"